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Metric properties of outer space
Francaviglia, Stefano (Università Bologna. Dipartimento di Matematica)
Martino, Armando (University of Southampton (Gran Bretanya). School of Mathematics)

Data: 2011
Resum: We define metrics on Culler-Vogtmann space, which are an analogue of the Thurston metric and are constructed using stretching factors. In fact the metrics we study are related, one being a symmetrised version of the other. We investigate the basic properties of these metrics, showing the advantages and pathologies of both choices. We show how to compute stretching factors between marked metric graphs in an easy way and we discuss the behaviour of stretching factors under iterations of automorphisms. We study metric properties of folding paths, showing that they are geodesic for the non-symmetric metric and, if they do not enter the thin part of Outer Space, quasi-geodesic for the symmetric metric.
Drets: Tots els drets reservats
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: Outer space ; Free group ; Lipschitz metric ; Stretching factor ; Optimal maps
Publicat a: Publicacions Matemàtiques, Vol. 55, Núm. 2 (2011) , p. 433-473, ISSN 0214-1493

Adreça original:
DOI: 10.5565/PUBLMAT_55211_09
DOI: 10.5565/244963

41 p, 530.9 KB

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